Method of DifferentiationmediumFree

Method of Differentiation — JEE Maths practice question

JEE Maths question with a full step-by-step solution.

Question
If y=(sin⁡−1x)2+(cos⁡−1x)2y = (\sin^{-1}x)^2 + (\cos^{-1}x)^2, then (1−x2)d2ydx2−xdydx(1 - x^2)\dfrac{d^2 y}{dx^2} - x\dfrac{dy}{dx} is:
A−4-4
B44correct
C22
D00
Solution
Step 1: First derivative
y1=2sin⁡−1x1−x2−2cos⁡−1x1−x2  ⟹  1−x2 y1=2(sin⁡−1x−cos⁡−1x)y_1 = \frac{2\sin^{-1}x}{\sqrt{1 - x^2}} - \frac{2\cos^{-1}x}{\sqrt{1 - x^2}} \implies \sqrt{1 - x^2}\, y_1 = 2(\sin^{-1}x - \cos^{-1}x)
 Step 2: Differentiate again
1−x2 y2−x1−x2 y1=2(11−x2+11−x2)=41−x2\sqrt{1 - x^2}\, y_2 - \frac{x}{\sqrt{1 - x^2}}\, y_1 = 2\left(\frac{1}{\sqrt{1 - x^2}} + \frac{1}{\sqrt{1 - x^2}}\right) = \frac{4}{\sqrt{1 - x^2}}
 Step 3: Multiply through by 1−x2\sqrt{1 - x^2}
(1−x2)y2−xy1=4(1 - x^2)y_2 - x y_1 = 4
 Answer: (2)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Method of Differentiation · easy
If y= 1+x 2 +x 4 1+x+x 2 and dy dx =ax+b , then the values of a and b are
Method of Differentiation · easy
If f(x) = | x| , then f' ( 3 4 ) is:
Method of Differentiation · easy
If f(x)= x , then f'( x) equals
Method of Differentiation · easy
d dx [ x + x 1 + 2x ] , where 0 < x < 4 , is:

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath